Approaches to the Monopole-Dynamic Dipole Vacuum Solution Concerning the Structure of its Ernst's Potential on the Symmetry Axis

The FHP algorithm allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst's potential on the symmetry axis. First of all, we will use this result in order to determine, at a certain approximation degree, the Ernst's potential on the symmetry axis of the metric whose only multipole moments are mass and angular momentum. By using Sibgatullin's method we analyse a series of exacts solutions with the afore mentioned multipole characteristic. Besides, we present an approximate solution whose Ernst's potential is introduced as a power series of a dimensionless parameter. The calculation of its multipole moments allows us to understand the existing differences between both approximations to the proposed pure multipole solution.Comment: 24 pages, plain TeX. To be published in General Relativity and Gravitatio

Anosov representations: Domains of discontinuity and applications

The notion of Anosov representations has been introduced by Labourie in his study of the Hitchin component for SL(n,R). Subsequently, Anosov representations have been studied mainly for surface groups, in particular in the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this article we extend the notion of Anosov representations to representations of arbitrary word hyperbolic groups and start the systematic study of their geometric properties. In particular, given an Anosov representation of $\Gamma$ into G we explicitly construct open subsets of compact G-spaces, on which $\Gamma$ acts properly discontinuously and with compact quotient. As a consequence we show that higher Teichmueller spaces parametrize locally homogeneous geometric structures on compact manifolds. We also obtain applications regarding (non-standard) compact Clifford-Klein forms and compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica

Wastewater-based epidemiology to assess pan-European pesticide exposure

Human biomonitoring, i.e. the determination of chemicals and/or their metabolites in human specimens, is the most common and potent tool for assessing human exposure to pesticides, but it suffers from limitations such as high costs and biases in sampling. Wastewater-based epidemiology (WBE) is an innovative approach based on the chemical analysis of specific human metabolic excretion products (biomarkers) in wastewater, and provides objective and real-time information on xenobiotics directly or indirectly ingested by a population. This study applied the WBE approach for the first time to evaluate human exposure to pesticides in eight cities across Europe. 24 h-composite wastewater samples were collected from the main wastewater treatment plants and analyzed for urinary metabolites of three classes of pesticides, namely triazines, organophosphates and pyrethroids, by liquid chromatography-tandem mass spectrometry. The mass loads (mg/day/1000 inhabitants) were highest for organophosphates and lowest for triazines. Different patterns were observed among the cities and for the various classes of pesticides. Population weighted loads of specific biomarkers indicated higher exposure in Castellon, Milan, Copenhagen and Bristol for pyrethroids, and in Castellon, Bristol and Zurich for organophosphates. The lowest mass loads (mg/day/1000 inhabitants) were found in Utrecht and Oslo. These results were in agreement with several national statistics related to pesticides exposure such as pesticides sales. The daily intake of pyrethroids was estimated in each city and it was found to exceed the acceptable daily intake (ADI) only in one city (Castellon, Spain). This was the first large-scale application of WBE to monitor population exposure to pesticides. The results indicated that WBE can give new information about the “average exposure” of the population to pesticides, and is a useful complementary biomonitoring tool to study population-wide exposure to pesticides

Model-based analysis of myocardial strains in left bundle branch block

International audienceIntroduction: Although observational studies of patients with left bundle branch block (LBBB) have shown a relation between strain morphologies and responses to cardiac resynchronization therapy (CRT), the evaluation of left ventricle (LV) dyssynchrony from echocardiography remains difficult. The objective of this article is to propose a patient-specific model-based approach to improve the analysis and interpretation of myocardial strain signals. Methods: A system-level model of the cardiovascular system is proposed, integrating: (i) the cardiac electrical system, (ii) right and left atria, (iii) a multi-segment representation of the RVs and LVs, and (iv) the systemic and pulmonary circulations. After a sensitivity analysis step, model parameters were identified specifically for each patient. The proposed approach was evaluated on data obtained from 10 healthy subjects and 20 patients with LBBB with underlying ischemic (n = 10) and non-ischemic (n = 10) cardiomyopathies. Results: A close match was observed between estimated and observed strain signals, with mean RMSE respectively equal to 5.04 ± 1.02% and 3.90 ± 1.40% in healthy and LBBB cases. The analysis of patient-specific identified parameters, based on bull's-eye representation, shows that strain morphologies are related to both electrical conduction delay, and heterogeneity of contractile levels within the myocardium. Discussion: The model-based approach improve the interpretability echocardiography data by bringing additional information on the regional electrical and mechanical function of the LV. The analysis of model parameters show that septal motion and global strain morphologies are not only explained by electrical conduction delay but also by the heterogeneity of contractile levels within the myocardium. The proposed approach represents a step forward in the development of personalized LV models for the evaluation of LV dyssynchrony in the field of CRT. Copyright © 2022 Taconné, Owashi, Galli, Duchenne, Hubert, Donal, Hernàndez and Le Rolle